C | math4u.vsb.cz

9000036105

Level:

The side

b

in the triangle

A B C

17 cm

and the angle

β

58^{\circ}

. Find the radius of the circle circumscribed to this triangle and round your answer to the nearest centimeters.

10 cm

8 cm

9 cm

11 cm

9000035607

Level:

Identify the quadratic equation with solutions

x_{1} = 2 i

x_{2} = - i

x^{2} - i x + 2 = 0

x^{2} + i x + 2 = 0

x^{2} + i x - 2 = 0

x^{2} - i x - 2 = 0

9000035608

Level:

The equation

x^{2} - 2 i x + q = 0

with a parameter

q \in C

has a solution

x_{1} = 1 + 2 i

. Find the second solution

x_{2}

and the parameter

q

x_{2} = - 1, q = - 1 - 2 i

x_{2} = - 1 - 4 i, q = 9 - 6 i

x_{2} = 1 - 4 i, q = 7 - 4 i

x_{2} = 1, q = - 1 - 2 i

x_{2} = - 1, q = 1 + 2 i

9000036101

Level:

3 m

long rod is in a slant position with respect to the observer's eye: one end is in the distance

20 m

and the other one

18 m

. Find the visual angle of the rod (the angle between the lines which connect the observer's eye and the ends of the rod) and round to the nearest degrees.

7^{\circ}

3^{\circ}

45^{\circ}

83^{\circ}

9000036102

Level:

Three forces act on the same body in the same point and the total force on the body is zero (the forces cancel). The first two forces are

8 N

and

10 N

and the angle between these forces is

55^{\circ}

. Find the third force.

16 N

15 N

17 N

18 N

9000036103

Level:

Three forces

F_{1}

F_{2}

and

F_{3}

act on the same body in the same point and the total force on the body is zero (the forces cancel). The first two forces are

F_{1} = 8 N

and

F_{2} = 10 N

and the angle between

F_{1}

and

F_{2}

55^{\circ}

. Find the angle between

F_{3}

and

F_{1}

. Round your answer to the nearest degrees.

149^{\circ}

125^{\circ}

55^{\circ}

30^{\circ}

9000036106

Level:

Two straight roads go off from the crossing. The angle between directions of the roads is

52^{\circ} 18^{'}

. A significant tree is on the first road in the distance

250 m

from the crossing. A rock with a beautiful view is on the second road in the distance

380 m

from the crossing. Find the direct distance (length of a line segment) from the rock to the tree and round your answer to nearest meters.

301 m

411 m

568 m

629 m

9000035602

Level:

Find the values of the parameter

m \in C

which guarantee that the following quadratic equation has a double solution.

m x^{2} - 2 x - 1 + i = 0

m = - \frac{1}{2} - \frac{1}{2} i

m = - 1

m = - 1 + i

m = - \frac{1}{2} + \frac{1}{2} i

9000033810

Level:

Find the parity (odd/even) of the function

l : y = | cotg x |

The function

l

is an even function.

The function

l

is an odd function.

The function

l

is neither an odd nor even function.

9000034303

Level:

Find the solution set of the following equation in the set of complex numbers.

x^{3} + i = 0

{i; \frac{\sqrt{3}}{2} - \frac{1}{2} i; - \frac{\sqrt{3}}{2} - \frac{1}{2} i}

{- 1; - \frac{\sqrt{3}}{2} + \frac{1}{2} i; - \frac{\sqrt{3}}{2} - \frac{1}{2} i}

{- 1; \frac{\sqrt{3}}{2} - \frac{1}{2} i; - \frac{\sqrt{3}}{2} - \frac{1}{2} i}

{i; - \frac{\sqrt{3}}{2} + \frac{1}{2} i; - \frac{\sqrt{3}}{2} - \frac{1}{2} i}

C

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